Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define REP(a,b) for(long long a = 0;a < b;++a)
int main(){
	int n;
	cin >> n;
	vector<double> wow;
	REP(i,n){
		double tmp;
		cin >> tmp;
		wow.push_back(tmp);
	}
	double ans = 0;
	sort(wow.begin(),wow.end(),greater<double>());
	for(int i = 0;i < wow.size()-1;++i){
		for(int q = i+1;q < wow.size();++q){
			double puu = 0;
			for(int j = 0;j < wow.size();++j){
				if(j != i&&j != q){
					if(puu != 0){
						puu += wow[j];
						break;
					}
					puu += wow[j];
				}
			}
			ans = max(ans,puu / abs(wow[i]-wow[q]));
		}
	}
	cout << fixed << setprecision(20) << ans << endl;
	return 0;
}